Repeated disconnection with multi connections

I wasn't able to find exactly the same issue posted somewhere else, but please link me if a solution is available.

Currently, my girlfriend and I play D3 while connected to the same LAN. We connect through the same router and modem, and are running very similar machines (hers is a macbook pro, and mine an iMac, but mine is old enough such that the hardware is almost identical to hers). After a short amount of playing (we haven't clocked it to see if it is a perfect cycle), she is disconnected from the server, and needs to restart D3. My computer remains connected, and continues to play fine. I also perceive her game as very laggy, despite her saying that it is normal (a consequence of her always playing in a laggy game, I think).

Has this happened to anyone else? Any solutions you can think of? My first guess is that there is a problem with multiple connections attempting to send/receive data through my router, but I'm not really sure how to check that.